In mathematics, when we need to solve the ratio of one variable (usually expressed as X) to another variable (usually expressed as Y), we can use the proportional function to express this relationship. The proportional function is usually expressed in the form of y/x, where y is the dependent variable and x is the independent variable. Proportional function can be used to describe the relationship in many practical problems, such as cost and output, speed and time, price and quantity.

In practical application, the proportional relationship is usually not a simple linear relationship, but is obtained through certain analysis and deduction. At this time, we can use proportional function to describe this relationship more accurately. The general form of the proportional function can be expressed as:

y=kx

Where y is the dependent variable (usually the large number in the proportion), x is the independent variable (usually the decimal or count in the proportion), and k is the proportional constant (usually the ratio of the proportion). Proportional constant represents the relationship between y and x, and is a fixed value, which can be obtained through observation or experiment in practical problems.

The characteristic of the proportional function is that when the independent variable X increases (or decreases), the dependent variable Y also increases (or decreases) proportionally, and the proportional constant K determines the proportional size of this relationship. Proportional function is usually used to describe the increase or decrease of linear proportional relationship. When the relationship between x and y is no longer a simple proportional relationship, we may need to use other types of functions to describe this complex relationship more accurately, such as polynomial function, exponential function, logarithmic function and so on.

In practical problems, the establishment of proportional relationship and the determination of proportional function usually need to be analyzed and studied according to specific conditions. Through observation and experimental data, we can get the value of the proportional constant k, and then establish a proportional function to describe the relationship between variables. Proportional function is widely used in solving practical problems, which helps us to better understand and describe the proportional relationship between different variables and provides a powerful mathematical tool for scientific research and engineering application.